Question 1068724
The law of cosines formula includes
3 side lengths and one angle.
Given 3 of those, you can find the fourth one,
so C and D look promising,
B would not work for ASA because ASA gives only one side length,
and A is ridiculous, because for AAA,
there is no way for any mathematician to guess the side lengths.
So, what about C and D.
Law of shines is easier to apply,
and can be applied whenever you have any 3 measurements,
including one angle and the opposite side.
That is what you have in SSA,
so for SSA you would use law of sines.
So, I vote for {{{highlight(C)}}} .
Besides, SSA can be tricky,
not only because you have to be careful not to accidentally spell it backwards,
but because there could be two different triangles with the same SSA.
{{{drawing(400,300,-36,24,-1,10,
green(triangle(-35,0,12,0,0,9)),
line(-35,0,0,9),red(line(12,0,0,9)),
red(line(0,9,-12,0)),locate(-35.5,0,A),
locate(-17,4.5,b)
)}}} If I give you angle A,
side b, and the length of the red sides,
how would you know which red side to choose?